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| Paper Abstract and Keywords | ||
| Presentation | 2024-05-09 10:45 Depth-Three Circuits for Inner Product and Majority Functions Kazuyuki Amano (Gunma Univ.)  COMP2024-4 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | A $Sigma_3^k$-circuit is a depth-three OR $circ$ AND $circ$ OR circuit in which each bottom gate has fan-in at most $k$. In this work, we investigate the $Sigma_3^k$-complexity for the inner product function the majority function and give the following two results. (i) We give an explicit construction of a $Sigma^2_3$-circuit of size smaller than $2^{0.952n}$ for $IP_n$, as well as a $Sigma^3_3$-circuit of size smaller than $2^{0.692n}$. (ii) We present a construction suggesting that the use of negations leads to a reduction in $Sigma_3^k$-complexity for $MAJ_n$. All these results rely on efficient circuits or formulas on a small number of variables that we found through a computer search. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Circuit complexity / Depth-three circuits / Upper bounds / Lower bounds / Computer-assisted proof / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 124, no. 12, COMP2024-4, pp. 9-9, May 2024. | |
| Paper # | COMP2024-4 | |
| Date of Issue | 2024-05-01 (COMP) | |
| ISSN | Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | COMP2024-4 |
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| Conference Information | |
| Committee | COMP IPSJ-AL |
| Conference Date | 2024-05-08 - 2024-05-09 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kyoto University (Rakuyu-kaikan) |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Theoretical Computer Science, etc. |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2024-05-COMP-AL |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Depth-Three Circuits for Inner Product and Majority Functions |
| Sub Title (in English) | |
| Keyword(1) | Circuit complexity |
| Keyword(2) | Depth-three circuits |
| Keyword(3) | Upper bounds |
| Keyword(4) | Lower bounds |
| Keyword(5) | Computer-assisted proof |
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| 1st Author's Name | Kazuyuki Amano |
| 1st Author's Affiliation | Gunma University (Gunma Univ.) |
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| Speaker | Author-1 |
| Date Time | 2024-05-09 10:45:00 |
| Presentation Time | 20 minutes |
| Registration for | COMP |
| Paper # | COMP2024-4 |
| Volume (vol) | vol.124 |
| Number (no) | no.12 |
| Page | p.9 |
| #Pages | 1 |
| Date of Issue | 2024-05-01 (COMP) |
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